Algebra 2
Chapter 1 Vocabulary
identity - A statement that equates two equivalent expressions.
verbal model- A word equation that represents a real-life problem.
algebraic expression - An expression with variables.
exponent - The number in a power that represents the number of times the base
is used as a factor.
equation - A statement in which two expressions are equal.
terms - The parts of an algebraic expression that are added together.
numerical expression - An expression that consists of numbers, operations, and
grouping symbols.
variable - A letter that is used to represent one or more numbers.
value - The result when the variables in an algebraic expression are replaced by
numbers and the expression is simplified.
coordinate - The number that corresponds to a point on a number line.
rational numbers - Numbers that can be written as the ratio of two integers.
integers - The numbers ... , -3, -2, -1, 0, 1, 2, 3, ...
graph of a real number - The point on a number line that corresponds to a
number.
order of operations - Set of rules that gives the order in which operations should
be performed when evaluating expressions.
power - An expression such as 25, which represents 2 · 2 · 2 · 2 · 2 = 32.
Algebra 2
Chapter 2 Vocabulary
independent variable - The input variable in an equation.
range - The set of output values for the relation.
relation - A mapping, or pairing, of input values with output values.
step function - A piecewise function whose graph resembles a set of stair steps.
linear function - A function of the form y = mx + b where m and b are constants.
Its graph is a line.
piecewise function - A function represented by a combination of equations, each
corresponding to a part of the domain.
function - A relation with exactly one output for each input.
"x" intercept - The x-coordinate of the point where a line intersects the x-axis.
parallel lines - Two lines in a plane that do not intersect.
dependent variable - The output variable in an equation, which depends on the
value of the input variable.
domain - The set of input values for the relation.
slope - The ratio of vertical change (the rise) to horizontal change (the run) for a
nonvertical line.
Algebra 2
Chapter 3 Vocabulary
"y" intercept - If the graph of an equation intersects the y-axis at the point (0, b),
then the number b. Given the equation of the graph, it is the value of y when x =
0.
"
z" axis - The vertical line through the origin and perpendicular to the xycoordinate plane in a three-dimensional coordinate system.
three dimensional coordinate system - Is a coordinate system determined by
three mutually perpendicular axes.
octants - When taken pairwise, the axes of a three-dimensional coordinate
system form three coordinate planes that divide space into eight parts
objective function - In linear programming, the linear function that is optimized.
Linear combination - A method for solving linear systems. Step 1: Multiply one or
both of the equations by a constant to obtain coefficients that differ only in sign
for one of the variables. Step 2: Add the revised equations from Step 1.
Combining like terms will eliminate one of the variables. Solve for the remaining
variable. Step 3: Substitute the value obtained in Step 2 into either of the original
equations and solve for the other variable.
constraints - In linear programming, the linear inequalities that form a system.
optimization - A process in which you find the maximum or minimum value of
some variable quantity.
system two of linear equations - Two equations of the form Ax + By = C and Dx
+ Ey = F where x and y are variables, A and B are not both zero, and D and E
are not both zero.
feasible region - In linear programming, the graph of the system of constraints.
"x" intercept - The x-coordinate of the point where a line intersects the x-axis.
Given an equation of the line, it is the value of x when y = 0.
solution - An ordered pair (x, y) that makes the equation a true statement when
the values of x and y are substituted in the equation.
slope - The ratio of vertical change (the rise) to horizontal change (the run) for a
nonvertical line.
Algebra 2
Chapter 4 Vocabulary
column matrix - A matrix with only 1 column.
Cramer's rule - A method for solving a system of linear equations which uses
determinants of matrices.
solution - An ordered pair (x, 0) that satisfies each equation of the system.
equal matrices - Matrices that have the same dimensions and equal entries in
corresponding positions.
matrix - A rectangular arrangement of numbers in rows and columns.
dimensions - The number m of rows of a matrix by the number n of columns of a
matrix, written m x n.
constant term - A term that has no variable part.
entries - The numbers in a matrix.
zero matrix - A matrix whose entries are all zeros.
row matrix - A matrix with only 1 row.
square matrix - A matrix with the same number of rows and columns.
scalar - A real number by which you multiply a matrix.
Algebra 2
Chapter 5 Vocabulary
vertex - The point of a parabola that lies on the axis of symmetry.
radicand - The number or expression beneath a radical sign.
trinomial - An expression with three terms.
factoring - A process used to write a polynomial as a product of other
polynomials having equal or lesser degree.
parabola - The set of all points equidistant from a point called the focus and a
line called the directrix.
complex conjugates - Two complex numbers of the form a + bi and a - bi. Their
product is always a real number.
vertex form - The form y = a(x - h)2 + k where the vertex of the graph us (h, k)
and the axis of symmetry is x = h.
complex number - A number a + bi where a and b are real numbers and i is the
imaginary unit.
rationalizing - The process of eliminating a radical in the denominator of a
fraction by multiplying both the numerator and the denominator by an
appropriate radical.
monomial - An expression with one term.
binomial - An expression with two terms.
Algebra 2
Chapter 6 Vocabulary
fundamental theorem of algebra - If f(x) is a polynomial of degree n where n > 0,
then the equation f(x) = 0 has at least one root in the set of complex numbers.
repeated solution - For the equation f(x) = 0, if and only if the factor (x - k) has
degree greater than 1 when f is factored completely.
end behavior - The behavior of the graph of a function as x approaches positive
infinity or negative infinity.
standard form - The form of a polynomial function where the terms are written in
descending order of exponents from left to right.
polynomial long division - A method used to divide polynomials similar to the way
you divide numbers.
factoring by grouping - A method used to factor some polynomials with pairs of
terms that have a common monomial factor.
synthetic division - is a method used to divide a polynomial by an expression of
the form x - k.
quadratic form - The form au2 + bu + c where u is any expression in x.
"x" intercept - The x-coordinate of the point where a line intersects the x-axis.
Given an equation of the line, it is the value of x when y = 0.
remainder theorem - If a polynomial f(x) is divided by x - k, then the remainder is
r = f(k).
power - An expression such as 25, which represents 2 · 2 · 2 · 2 · 2 = 32.
factor theorem - A polynomial f(x) has a factor x - k if and only if f(k) = 0.
Algebra 2
Chapter 7 Vocabulary
relation - A mapping, or pairing, of input values with output values.
median - The middle number when n numbers are written in order. (If n is even, it
is the mean of the two middle numbers.)
statistics - Numerical values used to summarize and compare sets of data.
inverse functions - A relation and its inverse relation whenever both relations are
functions.
range - The difference between the greatest and least data values.
mode - The number or numbers that occur most frequently in a set of n numbers.
mean - The sum of n numbers divided by n. Also called average.
exponent - The number in a power that represents the number of times the base
is used as a factor.
measures of dispersion - Used statistics that tell you how spread out the data
are. They include the range and the standard deviation.
like radicals - Two radical expressions that have the same index and the same
radicand.
frequency distribution - A table that shows the frequencies for the intervals into
which data are grouped.
square root - What r is in r2 = s.
standard deviation - is the typical difference between the mean and a data value.
Algebra 2
Chapter 8 Vocabulary
relation - A mapping, or pairing, of input values with output values.
base - What b is in a function involving the expression bx where b is a positive
number other than 1.
natural logarithm - The logarithm with base e.
exponential function - involves the expression bx where the base b is a positive
number other than 1.
exponential decay function - is a function of the form f(x) = abx where a > 0 and 0
< b < 1 (decrease).
exponent - The number in a power that represents the number of times the base
is used as a factor.
growth factor - The quantity 1 + r in the exponential growth model y = a(1 + r)t
where a is the initial amount and r is the percent increase expressed as a
decimal.
base of power - The number in a power that is used as a factor.
inverse function - A relation and its inverse relation whenever both relations are
functions.
decay factor - The quantity 1 - r in the exponential decay model y = a(1 - r)t
where a is the initial amount and r is the percent decrease expressed as a
decimal.
function - A relation with exactly one output for each input.
power - An expression such as 25, which represents 2 · 2 · 2 · 2 · 2 = 32.
asymptote - A line that a graph approaches as you move away from the origin.
Algebra 2
Chapter 9 Vocabulary
joint variation - A relationship that occurs when a quantity varies directly as the
product of two or more other quantities
verbal model - A word equation that represents a real-life problem.
"y" intercept - If the graph of an equation intersects the y-axis at the point (0, b).
Given the equation of the graph, it is the value of y when x = 0.
complex fraction - A fraction that contains a fraction in its numerator or
denominator.
asymptote - A line that a graph approaches as you move away from the origin.
hyperbola - The set of all points P such that the difference of the distances from
P to two fixed points, called the foci, is constant.
branches - The two symmetrical parts of a hyperbola.
relation - A mapping, or pairing, of input values with output values.
"x" intercept - The x-coordinate of the point where a line intersects the x-axis.
Given an equation of the line, it is the value of x when y = 0.
direct variation - y = kx where k is a nonzero constant.
cross multiplying - A method of solving a simple rational equation for which each
side of the equation is a single rational expression. Equal products are formed by
multiplying the numerator of each expression by the denominator of the other.
Algebra 2
Chapter 10 Vocabulary
transverse axis - The line segment joining the vertices of the hyperbola.
circle - The set of all points (x, y) that are equidistant from a fixed point, called the
center.
hyperbola - The set of all points P such that the difference of the distances from
P to two fixed points, called the foci, is constant.
vertex - This point is the lowest or highest point on a parabola with a vertical axis
of symmetry and the leftmost or rightmost point on a parabola with a horizontal
axis of symmetry.
radius - The distance r between the center of the circle and any point (x, y) on the
circle.
directrix - Perpendicular to the axis of symmetry.
parabola - The set of all points equidistant from a point called the focus and a line
called the directrix.
minor axis - The line segment joining the two co-vertices of an ellipse.
ellipse - The set of all points P such that the sum of the distances between P and
two distinct fixed points, called foci, is a constant.
conic section - A curve formed by the intersection of a plane and a doublenapped cone.
co-vertices - The points of intersection of an ellipse and the line perpendicular to
the major axis at the center.
focus - Lies on the axis of symmetry of a parabola.
Algebra 2
Chapter 11 Vocabulary
terms - For a sequence of numbers, the numbers in the sequence.
geometric series - The expression formed by adding the terms of a geometric
sequence.
arithmetic sequence - A sequence in which the difference between consecutive
terms is constant.
rational numbers - Numbers that can be written as the ratio of two integers.
factorial - The expression n! and represents the product of all integers from 1 to
n.
range - The set of output values for the relation.
domain - The set of input values for the relation.
integers - The numbers ... , -3, -2, -1, 0, 1, 2, 3, ...
geometric sequence- A sequence in which the ratio of any term to the previous
term is constant.
function - A relation with exactly one output for each input.
finite sequence - A sequence that has a last term.
sequence - A function whose domain is a set of consecutive integers.
common difference - The constant difference between consecutive terms of an
arithmetic sequence.
finite differences - To decide whether y-values for equally-spaced x-values can
be modeled by a polynomial function.
series - The expression that results when the terms of a sequence are added.
Algebra 2
Chapter 12 Vocabulary
factorial - The expression n! and represents the product of all integers from 1 to
n.
symmetric distribution - A distribution in which the left half of the histogram
representing the distribution is a mirror image of the right half.
dependent events - Two events such that the occurrence of one affects the
occurrence of the other.
independent events - Two events such that the occurrence of one has no effect
on the occurrence of the other.
experimental probability - A calculation of the probability of an event based on
performing an experiment, conducting a survey, or looking at the history of an
event.
probability - A number between 0 and 1 that indicates the likelihood an event will
occur.
compound event - The union or intersection of two events.
combination - A selection of r objects from a group of n objects where the order
is not important.
standard deviation - The typical difference between the mean and a data value.
permutation - An ordering of objects.
fair game - A game for which the expected value is 0.
geometric probability - A type of probability found by calculating a ratio of two
lengths, areas, or volumes.
mean - The sum of n numbers divided by n. Also called average.
Algebra 2
Chapter 13 Vocabulary
circle - The set of all points (x, y) that are equidistant from a fixed point, called the
center.
parameter - A variable, usually denoted t, upon which two other variables
depend.
parametric equations - Are equations that express two variables in terms of a
third variable, called the parameter.
radius - The distance r between the center of the circle and any point (x, y) on the
circle.
sector - A region of a circle that is bounded by two radii and an arc of the circle.
co-terminal angles - Two angles in standard position with terminal sides that
coincide.
terminal side - The rotating ray of an angle.
central angle - An angle formed by two radii of a circle.
angle of depression - The angle from a horizontal line through an object A to a
line connecting object A and a lower object B.
radian measure - In a circle with radius r and center at the origin, The measure of
an angle in standard position whose terminal side intercepts an arc of length r.
domain - The set of input values for the relation.
Algebra 2
Chapter 14 Vocabulary
local minimum - The y-coordinate of a turning point of the graph of a function if
the point is lower than all nearby points.
frequency - The reciprocal of the period.
domain - The set of input values for the relation.
relation - A mapping, or pairing, of input values with output values.
identity - A statement that equates two equivalent expressions.
period - The horizontal length of each cycle of a periodic function.
"y" intercept - If the graph of an equation intersects the y-axis at the point (0, b).
Given the equation of the graph, it is the value of y when x = 0.
local maximum - The y-coordinate of a turning point of the graph of a function if
the point is higher than all nearby points.
quadratic form - The form au2 + bu + c where u is any expression in x.
range - The set of output values for the relation.
function - A relation with exactly one output for each input.
"x" intercept - The x-coordinate of the point where a line intersects the x-axis.
Given an equation of the line, it is the value of x when y = 0.
asymptote - A line that a graph approaches as you move away from the origin.
cycle - The shortest repeating portion of a periodic function.